fix: make read_csv be able to read large numbers into float

Author: Alvaro-Kothe

pandas/_libs/parsers.pyx

@@ -1081,10 +1081,9 @@ cdef class TextReader:
                         np.dtype("object"), i, start, end, 0,
                         0, na_hashset, na_fset)
                 except OverflowError:
-                    col_res, na_count = self._convert_with_dtype(
-                        np.dtype("object"), i, start, end, na_filter,
-                        0, na_hashset, na_fset)
-
+                    # Try other dtypes that can accommodate large numbers.
+                    # (e.g. float and string)
+                    pass
                 if col_res is not None:
                     break
 

pandas/tests/io/parser/common/test_float.py

@@ -77,3 +77,28 @@ def test_too_many_exponent_digits(all_parsers_all_precisions, exp, request):
         expected = DataFrame({"data": [f"10E{exp}"]})
 
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "value, expected_value",
+    [
+        ("18446744073709551616.5", (1 << 64) + 0.5),
+        ("18446744073709551616", float(1 << 64)),
+    ],
+    ids=["2pow64_plus_half", "2pow64"],
+)
+def test_small_int_big_number(
+    all_parsers_all_precisions, value, expected_value, request
+):
+    # GH#51295
+    parser, precision = all_parsers_all_precisions
+    if parser.engine == "python" and value == "18446744073709551616":
+        mark = pytest.mark.xfail(reason="Still need to work on Python parser")
+        request.applymarker(mark)
+    data = f"""data
+    42
+    {value}"""
+    result = parser.read_csv(StringIO(data), float_precision=precision)
+    expected = DataFrame({"data": [42.0, expected_value]})
+
+    tm.assert_frame_equal(result, expected)